Based upon Monte Carlo simulations of amorphous molecular glasses, we have computed the electronic structure of five prototypical polyaromatic hydrocarbons using an extended Su-Schrieffer-Heeger model [J. R. Schrieffer, W. P. Su, and A. J. Heeger, Phys. Rev. Lett. 42, 1698 (1979)]. In the presence of excess charges, the resulting potential energy surfaces have been analyzed using Marcus' [Annu. Rev. Phys. Chem. 15, 155 (1964)] theory of charge transfer to yield reaction coefficients and--via the application of linear response theory--local conductivities. Applying Kirchhoff's rules, the emerging random resistor network problem leads to global conductivities of the order of 10(-1)-1 Scm, which correlate with the structural characteristics of the underlying geometry.